Cox, M G; Forbes, A B; Fossati, P M; Harris, P M; Smith, I M (2003) Techniques for the efficient solution of large scale calibration problems. NPL Report. CMSC 25/03

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Abstract

In this report, we describe algorithms and software for solving large scale calibration problems using nonlinear least squares approaches. We consider two approaches, one in which the sparsity structure can be exploited directly using matrix factorisation methods, the other in which iterative methods are used to solve the matrix equations involved. The former applies to systems that give rise to block-angular or banded matrices, for example, while the latter have more general application. Both approaches require modest algorithmic resources and can be encoded compactly in software and we provide specifications for some of the main software components. We compare the behaviour of these algorithms on a class of generalised regression problems. We also show how the use of solvers that employ harness components can be very effective in providing an interface between the user’s application and the optimisation software. We have implemented a simple Gauss-Newton solver using the harness approach and used it to solve a range of calibration problems employing both direct and iteration approaches.

Item Type:	Report/Guide (NPL Report)
NPL Report No.:	CMSC 25/03
Subjects:	Mathematics and Scientific Computing Mathematics and Scientific Computing > Modelling
Last Modified:	02 Feb 2018 13:16
URI:	http://eprintspublications.npl.co.uk/id/eprint/2779

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